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Russian Journal of Mathematical Physics

, Volume 25, Issue 4, pp 423–433 | Cite as

Dynamics of the Chaplygin ball on a rotating plane

  • I. A. BizyaevEmail author
  • A. V. Borisov
  • I. S. Mamaev
Article

Abstract

This paper addresses the problem of the Chaplygin ball rolling on a horizontal plane which rotates with constant angular velocity. In this case, the equations of motion admit area integrals, an integral of squared angular momentum and the Jacobi integral, which is a generalization of the energy integral, and possess an invariant measure. After reduction the problem reduces to investigating a three-dimensional Poincaré map that preserves phase volume (with density defined by the invariant measure). We show that in the general case the system’s dynamics is chaotic.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • I. A. Bizyaev
    • 1
    • 2
    Email author
  • A. V. Borisov
    • 1
    • 2
  • I. S. Mamaev
    • 1
    • 3
  1. 1.Moscow Institute of Physics and TechnologyDolgoprudnyiRussia
  2. 2.Udmurt State UniversityIzhevskRussia
  3. 3.Izhevsk State Technical UniversityIzhevskRussia

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